STRONGLY P-CLEAN RINGS AND MATRICES

167
180

Öz

An element of a ring R is strongly P-clean provided that it can
be written as the sum of an idempotent and a strongly nilpotent element that
commute. A ring R is strongly P-clean in case each of its elements is strongly
P-clean. We investigate, in this article, the necessary and sufficient conditions
under which a ring R is strongly P-clean. Many characterizations of such
rings are obtained. The criteria on strong P-cleanness of 2 × 2 matrices over
commutative projective-free rings are also determined.